I can’t tell if this is trolling or not, but O = Orders lol

Let me just, ahem

1-2+3/(3+3)×2+3×6/3 = 1-2+3/(3+3)×2+1×6 = 1-2+3/(3+3)×2+6 = 7-2+3/(3+3)×2 = 7-2+3/(6+6) = 7-2+(1/2+1/2) = 5+(1/2+1/2) = 5+1=6

Ahh, yes, DMAMDSBA :P

Let's just say BODMAS/PEMDAS isn't all end-all be-all. They're good, but there's also better

For those interested, see: basic number properties

This is actually a generational thing. Millennials were taught “PEMDAS”:

1. Parenthesis
2. Exponent
3. Multiplication
4. Division
5. Addition
6. Subtraction

But younger generations have been taught “BEDMAS” instead:

1. Brackets
2. Exponent
3. Division
4. Multiplication
5. Addition
6. Subtraction

Notably, Division and Multiplication are swapped on PEMDAS and BEDMAS, to make this “both happen at the same time” more straightforward. But that only applies if the entire operation can happen at the same time.

For instance, let’s say 6/2(3) compared to 6÷2(3). At first glance, they both appear to be the same operation. But in the former, the 6 dividend would be over the entire 2(3) divisor. Which means you would need to simplify the divisor (by resolving the multiplication of 2•3) before you divide. So the former would simplify to 6/6=1, while the latter would divide first and become 3(3)=9.

Technically, if you wanted to be completely clear, you would write it using multiple parenthesis as needed. For instance, you would write it as either:
(6÷2)(3)=9 or 6÷(2(3))=1 to avoid the ambiguity. Then it wouldn’t matter if you’re using PEMDAS or BEDMAS.

Usually, no sign before the bracket means juxtaposition. Scientific calculators do account for it (not all, tho), while regular ones may not.

So 2(1+2) is really (2+4)

Compare 2/2x and 2/2×X where x is (1+2)

The first is 2/(2+4)=1/3, the second is (2/2)×(1+2)=3

Basically, either 1 or 9 can be considered correct. And yes, it's ambiguous.

Also, there's no real rule about solving left to right due to associative and commutative properties: 1×2×3 = 1×(2×3) = (1×2)×3 = 3×1×2 = 2×1×3 = 6

would you say the same thing if the division was written out like a line under 2(3) and under that 6
idk how this'll come out but something like this:
2(1+2)
-----------
6

edit : wow i did a formatting thing
edit2: i got it (ish)

Only if you forget that multiplication happens left to right and that a(b) is simply a different way to write a×b with no other extra steps or considerations. The P in PEMDAS just means resolve what's INSIDE the parentheses first.

I’m guessing confusion is coming from those taking PEMDAS literally as that order? Rather than PE(M|D)(A|S), like it’s supposed to be?

I'm my head cannon, I imagine it as a /. Where the left is the top of a fraction, and the right the bottom. This only works in very simple equations though.

This is the correct answer and it drives me crazy how often this comes up.

As another user commented, division and subtraction are just syntactic flavor for multiplication and addition, respectively. Division is a specific type of multiplication. Subtraction is a specific type of addition.

And so there is a reason mathematicians do not use the division symbol (➗): it is ambiguous as to which of the following terms are in the divisor and which are part of the next non-divisor term.

In other words, the equation as written is a lossy representation of whatever actual equation is being described.

tl;dr: the equation as written provides insufficient information to determine the correct order of operations. It is ambiguous notation and should not be used.

CASIO calculators say 1, and I think it's more intuitive with "÷2π" being equivalent to "÷(2×π)" rather than "÷2×π". It took me a while to figure out why my results were almost but not quite one order of magnitude wrong after I was forced to switch to TI.